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  RE: https://mstdn.social/@QuantaMagazine/117359884077976693 Graham’s conjecture (1971): Modulo some prime p, can you find a way to order any subset of {1,...,p-1} so that its successive partial sums are all distinct? Since an initial breakthrough in 2022, three groups of young mathematicians have proved* this for different regimes: large subsets (as a fraction of p), small subsets, and finally those of intermediate size, covering all cases. *Like many results in combinatorics, the proofs only...

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  “So much for free speech. The studio releasing Alex Gibney’s new Elon Musk documentary Musk is finding itself unable to buy an ad on the biggest social platforms.” https://www.hollywoodreporter.com/business/digital/elon-musk-documentary-trailer-rejected-tiktok-youtube-1236710259/

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  TIL from @dandkuniverse.bsky.social that you can sometimes hear meteors burning up in the atmosphere *at the same time as you see them*, despite the discrepancy in the speed of light and the speed of sound. How? Here is an abstract from a relevant paper: “Recorded for centuries, people can hear and see meteors nearly concurrently. Electromagnetic energy clearly propagates at the speed of light and converts to sound (called electrophonics) when coupled to metals. An explanation for the electrom...

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  “I’d created 2000 free-text responses and labelled them ‘UK’. Then I copied and pasted the exact same 2000 responses but labelled these ‘US’. Finally, I combined them to create a dataset of 4000 total responses, and jumbled them up. Despite the responses being identical for the UK and US, Copilot produced a rich, detailed summary of how US and UK respondents differed.” https://kucharski.substack.com/p/real-signals-or-artificial-stereotypes H/T @sinalana.eurosky.social

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  Open Letter about the Mathathon This open letter calling for the cancellation of the Caltech “Mathathon”, has received 471 signatures so far. [Only members of the Caltech community or mathematicians at PhD student level or beyond are eligible to sign.] “On October 30th, 2026, Caltech will begin hosting the Caltech Mathathon, a math hackathon in which participants are encouraged to solve open research problems by prompting LLMs. Two prominent AI companies, Anthropic and OpenAI, will supply part...

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  Data centres powered by gas or coal should be 100% steampunk, full of hissing, clanking Babbage engines, tended by grimy-faced urchins who risk being crushed between the gears as they clear out all the sparrow's-nest malware with chimney-sweep brushes. https://www.abc.net.au/news/2026-08-06/ai-data-centres-gas-northern-territory/107002860

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  The fatal Hendra virus was an infamous spillover from bats to horses to humans in Australia in the 1990s. Since then, ecologists, bat experts and virologists have learned a lot about these events, perhaps including mitigating strategies. “The findings suggested that planting eucalyptus trees that feed bats in winter, when food elsewhere is scarce, could help prevent spillover by drawing bats from all over the country. When there are rare pulses of flowering in remnant winter habitat, the bats l...

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  “All previous identifications of asteroids with a neck have been interpreted as ‘bilobates’, having just two lobes, but (44) Nysa has a unique ‘trilobate’ structure.” https://www.eso.org/public/videos/potw2631a/

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  While the Fields Medal celebrates the under-40s, the mathematician Joan Birman has, at the age of 99, solved a major open problem in representations of the Braid groups, a topic she has worked on for more than 60 years. An element of the Braid group 𝐵ₙ is a way of joining two sets of n points with strings, where two elements are the same if the strings can be moved around and/or stretched to follow the same paths in 3-dimensional space while keeping their endpoints fixed. The Burau representat...

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  In 1909, Arthur Wieferich proved that if 𝑥ᵖ+𝑦ᵖ=𝑧ᵖ for an odd prime 𝑝 that does not divide positive integers 𝑥, 𝑦, or 𝑧, then 𝑝² must divide 2ᵖ⁻¹−1 Fermat’s little theorem says 𝑝 itself always divides 2ᵖ⁻¹−1. Soon afterwards, Dmytro Grave checked every prime under 1000, and conjectured that no such “Wieferich Primes” exist! Then in 1913, Waldemar Meissner checked 1093 … Now that we have computers this is trivial, but in 1913 it was a slog. Meissner showed that 2³⁶⁴−1 was divisible by 1093²...

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  Australia is planning to replace SMS-based emergency alerts with a new system. There will be a test on Monday 27 July at 2pm AEST. https://www.ausalert.gov.au/alerts-explained/national-test “Will my device receive an AusAlert? AusAlerts work on many mobile phones, tablets and smartwatches. Devices don’t need a working SIM card. They are expected to work on: • iPhones 11 and up running iOS 26.4 or later • Apple Watch SE2, SE3, Series 6 and up running watchOS 26.4 or later • Android devices ru...

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  The Jacobian conjecture is false! The Jacobian conjecture proposed that if you have a map F:C^n→C^n with polynomials as the components, and the determinant of the matrix of partial derivatives of F is a non-zero constant, then F will have a polynomial inverse. https://en.wikipedia.org/wiki/Jacobian_conjecture But someone has now found a counterexample. This is easy to check, so there’s no doubt that it’s correct. https://x.com/__alpoge__/status/2079028340955197566 𝐹(𝑥,𝑦,𝑧) = (𝑦²(3𝑥𝑦+4)(𝑥𝑦+1...

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  An interesting interview with former US Energy Secretary Ernest Moniz, a nuclear physicist who was involved in the negotiations leading to the 2015 Iran nuclear agreement. His Iranian counterpart, Ali Akbar Salehi, had studied at MIT when Moniz was on the faculty, and though they hadn’t met at the time they had many friends in common. (25 min audio) https://www.abc.net.au/listen/programs/if-youre-listening/is-trump-pushing-more-countries-toward-nuclear-weapons-/106911218

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  While the FCC has approved a test satellite from Reflect Orbital (which wants to illuminate solar farms at night), the basic physics here seems decisive — on the side of “No, this can’t possibly be a practical thing to do.” From the linked analysis by Michael Brown and Matthew Kenworthy: [Reflect Orbital’s plan is “simple satellites in the right constellation shining on existing solar farms”. And their goal is only 200 watts per square metre – 20% of the midday Sun. Can smaller satellites del...

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  “In the 80 years since George Romero's Night Of The Living Dead ambled into public consciousness … ” So Romero managed to insinuate his movie into the zeitgeist when he was six years old, 22 years before it was released. That’s one hell of a slow-burn viral marketing campaign. Quote is from the preamble to an interview with Yeon Sang-ho, director of “Train to Busan” [which I loved] and the new film “Colony” [not yet seen]. https://www.abc.net.au/news/2026-06-20/yeon-sang-ho-colony-the...

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  I’m two episodes into “For the Record: An Incomplete History of Music” from the Cosmic Shambles. It’s a sprawling, joyful, smart and generous tour, from the baryonic acoustic oscillations of the early universe to the Pythagorean comma, the Indian Tala system, Arabic quarter-notes, and much more to come (9 episodes in total, not all of them yet released). https://www.youtube.com/playlist?list=PLoVTI-iJf1y2EfoTD-fOQLfQ3hQunroWy

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  We have observed electron neutrinos oscillating into mu and tau neutrinos. But could we ever observe electrons themselves oscillating into muons or tauons? The short answer is “probably not”, for reasons mostly to do with the much greater mass differences between the charged leptons compared to those of the neutrinos. But it’s worth reading this paper in full, as it gives a clear, detailed exposition of the creation, propagation and detection of the relevant states. H/T Martin Bauer https:/...

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  AI-assisted answers to Erdős conjectures get all the buzz, but good old-fashioned human mathematicians [*] recently settled a 50-year-old conjecture: Is there a positive constant c such that every binomial coefficient Bin(n,k) has a divisor in the interval (cn,n]? The answer turns out to be: YES when n is large and k is large compared to n, but strictly NO. It's a long proof, but I managed to learn something cool from the first few pages. Erdős originally guessed that maybe Bin(n,k)...

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  “Mathematician Laurence Sigler had made it his mission to translate [Fibonacci’s Liber Abaci], rushing to complete the task right before he died of lymphocytic leukemia in 1997. But his editor moved on, and the manuscript languished on floppy disks for years. For a while Sigler’s widow Judith Sigler Fell, fearing the project would be killed, took the extraordinary step of impersonating her husband in communiqués. By the time Fell found a new publisher, Springer Verlag (now part of the same publ...

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  TIL that the sea-sickness medication that made the D-day landing possible — given the loss of usual supplies from Europe — was derived from a native Australian plant, the corkwood tree Duboisia myoporoides, whose properties had been known for centuries to indigenous Australians. https://www.abc.net.au/listen/programs/no-one-saw-it-coming/dday-bush-medicine/106778814 https://www.kcl.ac.uk/news/australian-indigenous-bush-medicine-was-given-to-allied-soldiers-on-d-day https://en.wikipedia.org/wi...

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  My phone acquired a handful of odd bugs yesterday (unable to use mobile data, 3-button navigation not working, quick settings panel limited to one row) after being present [switched off] in the room where I had a CAT scan. A factory reset got everything back to normal. I suppose it could be a coincidence, but if it wasn’t, I hope all the computing hardware crucial to the scanner itself was better shielded against whatever spillage corrupted the phone's flash storage. Here’s a study on the...

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  Phase contrast microscopes were invented in the 1930s by the Dutch physicist Frits Zernike, and developed and manufactured by physicist and entrepreneur Caroline “Lili” Bleeker. Zernike won the Nobel Prize for this in 1953 ... but Bleeker held the patents, so she might not have been too disappointed. The picture here shows how converting the *phase shift* in the light passing through an almost transparent cell into a *change in brightness* can improve the contrast and detail in the image. http...

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  Lots of regrettable silliness here: two papers by Max Planck (!) have been retracted, probably by some automated process that based the decision on the same material appearing in another journal (which was far more common at the time, and even Einstein did it) and a rebuttal to a work being published under the same title (but not author) as the thing being rebutted. But the funniest line in the article is: “Springer Nature is nevertheless still selling the empty PDF for $39.95.” https://www.s...

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  I think this is well worth reading. I've been a bit frustrated by some over-confident claims that data centres in space are literally impossible due to the cooling issues alone, and other claims that those issues are fairly minor. I am nowhere near close to being familiar with all the real-world engineering nitty gritty; I understand a fair bit of thermodynamics, but that is not enough to really settle things. FWIW, the arguments here seem well grounded in physics and the technological/econo...

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  For people who prefer audio: https://clarkesworldmagazine.com/audio_10_25c/

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  Erratum: An alert reader found a mistake in the answer I gave in the story to the jelly bean problem. The correct answer is that it takes between 2 and 3 samples to fix the position of the chutes, with an average of 2⅓.

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  Dear Benjamin Franklin I have travelled back in time from 2026 to tell you that we’re still not certain exactly how lightning works. There are relativistic electrons and gamma rays involved, maybe positrons, and (possibly extragalactic) cosmic rays. But it’s complicated, and we’re still thrashing out the details. https://www.quantamagazine.org/what-causes-lightning-the-answer-keeps-getting-more-interesting-20260506/

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  First it was my neighbours’ airconditioner showing up in my WiFi lists, now it’s their “55-inch Samsung The Frame QLED 4K TV” showing up in my Bluetooth. No wonder would-be burglars drive around with Bluetooth scanners looking for things to steal.

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  Breaking: Google AI summary of leaked Australian budget papers confirms that $2B will be allocated to phasing out all bicycle gears that rotate in the wrong direction by 2035.

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  A new knot invariant that “uniquely identifies more than 97% of the knots with 18 crossings. By comparison, the Jones polynomial, one of the most widely used invariants for cataloging knots, identifies about 42%, and the Alexander polynomial only about 11%.” A great write-up in Quanta: https://www.quantamagazine.org/a-powerful-new-qr-code-untangles-maths-knottiest-knots-20260422/ The paper itself is fun and fairly accessible. It’s also full of questions for the future! “A Fast, Strong, Topol...